Soccer Players and Baseball Players Ratio in School Teams

What could be the number of players on each team?

Since the ratio of soccer players to baseball players on two school teams is 4 to 7, which of the following could be the number of players on each team?

Final answer:

Only the options '12 soccer players and 21 baseball players' and '16 soccer players and 28 baseball players' satisfy the given ratio of 4 to 7 for soccer players to baseball players.

What is a ratio?

In Mathematics, a ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

What is a proportion?

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Mathematically, the relationship between the ratio of soccer players to baseball players on the two school teams can be modeled by the following mathematical expression:

y = kx

Therefore, the constant of proportionality is given by;

k = y/x

k = 4/7

Multiplying both the numerator and denominator by 3, we have;

k = (4/7) × 3

k = 12/21

Explanation:

The ratio of soccer players to baseball players given is 4 to 7. This means that for every 4 soccer players, there are 7 baseball players. When we examine the options provided, we see that only the third (12 soccer players and 21 baseball players) and the last (16 soccer players and 28 baseball players) options satisfy this ratio. For example, in the third option, if we divide the number of soccer players (12) by 4, we get 3. We then multiply 7 (the number of baseball players in the ratio) by the same number (3), and we get 21, which is the number of baseball players in the third option. We repeat the same process for the last option and find it also satisfies the given ratio.